This is a question specific to Ashkenazim (Nusach Ashkenaz, Nusach Ari, and Nusach Sefard). On Shabbat, after the Torah Reading and before Mussaf, 3 prayers, (2 Yikkum Purkans and a Mi Sheberach) are ...
In many Siddurim and Maḥzorim Adon 'Olam is printed at the end of Ma'ariv for Friday night and Yom Tov. But in my experience, the vast majority of (Ashkenazi) Shuls sing Yigdal at this point instead. ...